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   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenge Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find the lowest common ancestor in a binary tree.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is this a binary search tree?\n",
    "    * No\n",
    "* Can we assume the two nodes are in the tree?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "          _10_\n",
    "        /      \\\n",
    "       5        9\n",
    "      / \\      / \\\n",
    "     12  3    18  20\n",
    "        / \\       /\n",
    "       1   8     40\n",
    "</pre>\n",
    "\n",
    "* 0, 5 -> None\n",
    "* 5, 0 -> None\n",
    "* 1, 8 -> 3\n",
    "* 12, 8 -> 5\n",
    "* 12, 40 -> 10\n",
    "* 9, 20 -> 9\n",
    "* 3, 5 -> 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.jupyter.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_lca/tree_lca_solution.ipynb).  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Node(object):\n",
    "\n",
    "    def __init__(self, key, left=None, right=None):\n",
    "        self.key = key\n",
    "        self.left = left\n",
    "        self.right = right\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BinaryTree(object):\n",
    "\n",
    "    def lca(self, root, node1, node2):\n",
    "        # TODO: Implement me\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The following unit test is expected to fail until you solve the challenge.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load test_lca.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestLowestCommonAncestor(unittest.TestCase):\n",
    "\n",
    "    def test_lca(self):\n",
    "        node10 = Node(10)\n",
    "        node5 = Node(5)\n",
    "        node12 = Node(12)\n",
    "        node3 = Node(3)\n",
    "        node1 = Node(1)\n",
    "        node8 = Node(8)\n",
    "        node9 = Node(9)\n",
    "        node18 = Node(18)\n",
    "        node20 = Node(20)\n",
    "        node40 = Node(40)\n",
    "        node3.left = node1\n",
    "        node3.right = node8\n",
    "        node5.left = node12\n",
    "        node5.right = node3\n",
    "        node20.left = node40\n",
    "        node9.left = node18\n",
    "        node9.right = node20\n",
    "        node10.left = node5\n",
    "        node10.right = node9\n",
    "        root = node10\n",
    "        node0 = Node(0)\n",
    "        binary_tree = BinaryTree()\n",
    "        self.assertEqual(binary_tree.lca(root, node0, node5), None)\n",
    "        self.assertEqual(binary_tree.lca(root, node5, node0), None)\n",
    "        self.assertEqual(binary_tree.lca(root, node1, node8), node3)\n",
    "        self.assertEqual(binary_tree.lca(root, node12, node8), node5)\n",
    "        self.assertEqual(binary_tree.lca(root, node12, node40), node10)\n",
    "        self.assertEqual(binary_tree.lca(root, node9, node20), node9)\n",
    "        self.assertEqual(binary_tree.lca(root, node3, node5), node5)\n",
    "        print('Success: test_lca')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestLowestCommonAncestor()\n",
    "    test.test_lca()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
   ]
  }
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